This volume is a review on the recent progresses done in the understanding of the physics of the superconducting arrays. It consists of five sessions:All the topical contributions go well beyond those characteristics of the condensed matter physics and offer links to the domains of the nonlinear science, complex systems and statistical mechanics.

Macroscopic quantum phenomena (MQP) occur in a number of different systems. The majority of MQP research is done with electromagnetic circuits. The occurrence of MQP in alternative systems, the effects of the environment on MQP, the implications of MQP for measurement theory and quantum mechanics are discussed. This proceedings should therefore provide a nice balance of up-to-date results of MQP research, along with discussion of its implications and possible applications.

This is a graduate text on functional analysis. After presenting the fundamental function spaces and their duals, the authors study topics in operator theory and finally develop the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems. Along the way, the reader is presented with a truly remarkable assortment of well formulated and interesting exercises, which test the understanding as well as point out many related topics. The answers and hints that are not already contained in the statements of the exercises are collected at the end of the book.

The search for microscopic models to explain the many superconducting substances has introduced seminal concepts and techniques in many-body physics and in statistical mechanics. The complexity of the high-temperature superconductors has required a remarkable refinement of experimental techniques in order to allow a reliable characterization of the samples, and is partly the reason why so many different microscopic models have so far been proposed. This Enrico Fermi Course on Superconductivity was provided an up-to date presentation of selected experimental and theoretical theories on the (so called) conventional superconductivity and on the high temperature superconductivity. The attention was focused on those reliable measurements which are expected to provide the theory with key constraints, viz: Raman and Infrared Spectroscopy, Nuclear Spin Resonance, Angular Resolved Photoemission Spectroscopy, transport measurements, Josephson effect. The lectures devoted to the overview of the BCS theory and to the discussion of minimal models and of the crossover from BCS to Bose-Einstein condensation may be particularly useful. The remaining part of the program was shared between phonon and non-phonon based mechanisms. On the one hand, special emphasis has been devoted to the breakdown of the Migdal theorem and to polaronic theories. On the other, the book contains an overview of strongly correlated electron theories, including magnetic interactions. A survey of the physics of vortices completes the theoretical part of the lectures.

The main focus of the book is to present the effects of nanostructuring on superconducting critical parameters. Optimizing systematically flux and condensate confinement in various nanostructured superconductors, ranging from single nano-cells to their huge arrays, critical fields and currents can be increased up to their theoretical limits, thus drastically improving the potential for practical applications of nanostructured superconductors.

The International Symposium on Superconductivity, which has been held annu ally since 1988, is a forum for presenting the most up-to-date information about a broad range of research and development in superconductivity, from funda mental aspects to applications. More than 10 years have passed since the discovery of oxide superconductors and since various developments of applications began. It may be said that the prospects for application of oxide superconductors recently have opened up. Great progress has been made toward practical use, for example, of the flywheel, which uses bulk materials, and the high-performance cryo-cooled magnet made of bismuth wire. These were the results of persistent efforts to develop materials from the viewpoint of materials science and engineering. Also important is the progress in comprehensive understanding of high temperature superconductivity. Unique electronic properties of cuprates such as the non-Fermi liquid normal state, spin-charge separation, spin gap, and d-wave symmetry were discussed at the symposium, as were the unique electromagnetic properties resulting from the low dimensionality of cuprates. In the field of new superconductors, many exotic materials have been discovered since 1986. A decade of work with cuprate superconductors is reviewed in this proceedings, and several of the newest materials are presented. These papers will be instructive for many researchers and for students who are to enter this field.